Law of Large Numbers, Variance, bet size/frequency

Setting and influencing the dice roll is just part of the picture. To beat the dice you have to know how to bet the dice. Whether you call it a "system," a "strategy," or just a way to play - this is the place to discuss it.

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mainframe
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Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Thu May 17, 2018 8:56 am

All,
I am looking for overall science/math-based advice on bet size and frequency.
I did some research on the "Law of Large Numbers". I think that the Law of Large Numbers is the Casino'owner's best friend because every game in the casino is a negative expectation game, or at best, a zero expectation game.

Sidebar- Fair bets don't hurt the house
Other than the "Free Odds" bet, Casinos have occasionally offered other "fair" craps bets that had a zero expected value. Apparently, the Santa Ana Star Casino in New Mexico used to offer a field bet that paid triple on both the 2 and 12, with an EV of 0. They supposedly still offer vig-free buy bets on the 4 and 10 (vig free regardless of outcome) As per the Law of Large numbers, a casino can offer a few zero EV wagers and not suffer because the expected loss is 0. If anything, 0 EV bets are just "overhead" or "a waste of time" for the casino.

Variance is the player's only hope of winning
Players in a casino are essentially hoping for the short-term variance in event outcomes to swing in their favor away from the true odds of an event(and EV associated with that event) in order to walk away a winner.
Craps, as a whole, is a high variance game (Unless you habitually hedge your bets, in which case you lower the game's built-in variance).

The more often you wager, the more closely the results will resemble the mathematical EV
The Law of Large numbers states/proves that the more frequently we wager at the craps table, the closer the outcomes will be to the true EV inherent in each bet. This is why booking bets with a lower negative EV will result in less loss of bankroll over time than booking bets with a higher negative EV. It is also why combining a series of bets with lower negative EV and higher negative EVs results in a larger drain on your bankroll than consistently booking lower negative EV bets like Pass/Come,Don't Pass/Don't Come.

Given all of the above, here is my question: For a high variance, negative expectation game of chance (Craps), is it better for a player to book a few large bets, or to book many smaller wagers. My thought process is that it is actually better to place one or a few large wagers, accept the outcome and walk away. Is that scientifically correct?

Placing a few large wagers "win or lose" and walking away is not much "fun" for people that enjoy the social aspects of the game, or for people that consider it to be a meditation to play long craps session.

mainframe
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Thu May 17, 2018 11:12 am

Irish: I am glad you found my post to be valuable and on-point. It's validating to have a long-term forum-member compliment my writing.
If this thread in fact captures the essence of "optimal bet size, frequency, and strategy" for any high-variance, negative expectation game of chance, then there really isn't much more to discuss in a gambling forum regarding "optimal strategy". I guess the one thing excluded from this thread thus far is how a game of chance that includes an "element of skill" can improve outcomes. Poker has an element of skill, as does card counting in blackjack. I would [[/i]think[/i] that empirically,"dice influencing" qualifies as well. But that's a whole different topic to discuss.

Regarding "Why do people gamble?" and "Why do people play craps"? You are correct that is a large topic unto itself.
For me, gambling is entertainment along with the illusive prospect of winning some money in the process. If the end-goal is to play a game of chance simply to maximize your chances of profit, the optimal approach would run counter to most people's play-style. I guess the true "all business" types would avoid craps altogether and stick to positive expectation wagers such as blackjack with card counting. Among the "all business" craps players, I would think they would consistently play only the Don't pass backed by the maximum lay amount allowed. Furthermore, they would make very few Don't pass wagers, with large bets, and have very short play sessions with very stringent win goals and loss limits.

mainframe
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Thu May 17, 2018 11:27 am

One more thought/question: I personally am always fascinated/enthralled by the concept of "grinding for comps". I know conventional wisdom is "don't gamble to run up comps, you'll spend a lot more money than you would if you paid for your buffet or hotel room out-of-pocket".
But given the example of the Santa Clara Star in New Mexico's 0 EV bets (field bet paying triple on both 2 & 2, and vig-free buy bets for 4/10), I wonder if that could have been a loophole to run up some major comps with the house. I also wonder if the craps pit at the Santa Clara Star even tracked play on the zero EV games.

mainframe
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Thu May 17, 2018 2:10 pm

Not being facetious here, Irish...But how exactly does one gain an edge at Craps? Are you referring to the illusive (but plausible) discipline of dice control/dice influence? Or are you referring to stealing chips from the bank when no one is looking? Albert Einstein supposedly once said "No one can win at roulette unless he steals money from the table while the croupier isn't looking."

Here is my intuitive thoughts on the concept of "Dice Influence":
From a physics perspective, the outcome of a dice throw is not a truly random event. Take the act of dropping the dice straight downward from a height of two feet with the dice held a certain way. Theoretically, if you knew all the physical level variables exactly (air resistance, gravity, materials involved, friction, etc) you could accurately predict exactly which face of the dice will end up on top of each cube. Practically speaking however, the process of calculating all of this so complex, that by consensus, the outcome is considered random. An interesting question in my mind is if a pseudo random number generated by a microcomputer produces a result that is more random or less random than a physical roll of the dice.See: https://www.insidescience.org/news/dice ... ely-random

Following the logic above, if you take at face value that throwing dice does not produce truly random results (but is approximated as random), it stands to reason that you can influence the outcome by setting the dice a certain way, gripping them a certain way, tossing them a certain way, with a certain force and throwing arc. Some authors on the topic of dice influence even say that there are people walking around who are naturally consistent in their throwing patterns that exert some degree influence even without lots of practice and formal study. Is the term "rhythm roller" acceptable in this forum? In my nomenclature, a rhythm roller unconsciously exerts influence over the outcome of a dice toss, while a dice influencer is consciously making an effort to do so and practices also hones and practices his/her throw.

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London Shooter
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by London Shooter » Thu May 17, 2018 4:54 pm

That's your edge - some kind of influence.

People are not beating the random game through bankroll size, money management, MP204, missing numbers, due numbers, "bets off" at any kind of happening around the table or its immediate environs, or whatever other flavour of voodoo is most prevalent that week.

The fundamental is edge. We had a thread a few months back about putting 5 or 6 factors in order of importance to be a successful gambler. Hardly anybody ranked edge as number 1.

DanF
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sat May 19, 2018 12:56 am

The only mistake you guys make saying this... variance is not the only chance of winning. Best chance of winning is regression betting & DI. If you can have a large sample of hands that give you two hits on primary number and bet them, it is your best chance of winning over time. Don’t go for rare long hands...play short hands good & progress long hands.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sat May 19, 2018 8:26 am

Regression betting will increase the number of winning sessions but reduce the amount of profit if you are pairing it with DI and playing with an edge. We've debunked the theory that losing less means winning more.
Debunked? How? I debunked the exact opposite. Which test is right?

This game average 6ish rolls. So you need to play a game that profit those and progress bigger hands.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sat May 19, 2018 10:58 am

Math is simple.

6 rolls average.
You need to lock profits under 6 rolls on most hands.
Don’t press first hit, lock it up cuz it reduce exposure of second. Lock profits on third hit. Win 140 on two bets for 190 invested. Reinvest 56$ And lock 84$ on most hands under 6 rolls. On the long run it does this:
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DanF
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sat May 19, 2018 11:13 am

46391 goes to 46608 in a few rolls. With 135$ on table on seven out.

20$ pass, 60$ 6&8, 50$ 9.
Lock first 70$ win,
Regress to 18$ 6&8+pass(made an error so I placed point.)
First hit up a unit, second hit all the way...have fun.

I did the system right away and it worked.

Rolls were:

11,4,12,4pass, 9, 8,11,8,10,5,6,8,8,6...7

So locked, 20$,20$,70$,70$,15$,15$ profits and had 135$ pressed on table. That ez 8th roll I profited 20$+20$+70$+70$-56$.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sun May 20, 2018 5:49 am

Ok, the above is real. It’s not a cash play, it’s an app I use for testing.

I don’t have much time on my hands in the last months...new baby girl, so I didn’t have long in casino yet... showing you cash won’t be a proof either...I could just have a good bankroll.

If you don’t believe me it’s your call, I don’t care.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sun May 20, 2018 5:54 am

I had two sessions lately with too many players on table to be profitable... still came up on top. Now I’m holding up for a gamble trip, which should be this summer. I work 50h a week and have 2 kids, so spare time isn’t part of my life much lol.

Moe Bettor
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by Moe Bettor » Sun May 20, 2018 9:19 am

I agree with part of your conclusions Dan..that regression early on randies is the way to go. However if you have a$20 PL..(Why would you have a PL bet on a randy?) $60 6 and 8 and $50 9 a 7 out will put you down $190 if I am understanding what you are doing. That means just to get even with your betting system working you'll pull $70 on the next try and regress to $18 6 and 8..It will take quite a good hand to just get you even. Many good hands. Putting $190 out there to win $70 is like a pretty severe "no 10" play..where you lay $150 to win $75. Which is ok under the right circumstances..but not always. Why not start with $18 6 and 8 no PL bet. Regress to $12 6 and 8 on hitting $21. You now have $3 at risk..or take two hits and be way ahead. Then press like a madman. Whatever happens, you are already ahead. Hey..eventually you may get enough ahead to make those larger across bets.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by London Shooter » Sun May 20, 2018 12:57 pm

I just tried the play on Wincraps and got handed my virtual ass with a bunch of PSOs and PPSOs. It's an interesting kind of play, as many are, but as with any system on the craps table NOTHING is beating the random game.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sun May 20, 2018 8:34 pm

I play this in casino only on my rolls and known successful thrower. But I know someone who does it on everyone so I tested it on the app and it usually handle itself okay. There are some losing streaks, but the winning ones usually overcomes it.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Sun May 20, 2018 8:39 pm

Also you can’t wincraps trend changes, I don’t exclusively use this play. Like I said before...if you want any chance in this game you need 5-6 good gameplans depending on situations. Sometimes I bet bigger, sometimes I bet smaller. Sometimes I go progressive, sometimes regressive. Sometimes I play darkside, sometimes I only lay the point/ build from only 1 bet, spreads...

Here’s how yesturday ended...
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mainframe
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Mon May 21, 2018 9:06 am

Guys,
I am not a mathematics wizard by any means. But there is no "fool proof" system, nor even a system that consistently wins money "most of the time" given a large enough sample size. You can go through life using any wagering system and have a bunch of "perceived success". But a gut instinct statement like "I win with this system most of the time" may mean that you have been extremely lucky in your table sessions, or that you haven't consistently and accurately tracked your play. The more events you gamble on, the more closely (statistically), the outcomes will be to the mathematical "expected value" of each individual wager.

We all talk about the concept of a "trend", a "hot shooter", etc...its so tangible you can almost taste it or feel it. But in mathematical terms, for a completely random event, a "trend" equates to is "Variance in outcome" coincidentally swinging in the player's favor instead of the casino's favor.
If someone had truly discovered a system of wagers that netted a positive expected value "most of the time", why wouldn't they just play a whole lot of craps using that system and grow their bankroll to a comfortable early retirement? And if a wagering system consistently netted you a win, wouldn't it get noticed, "get around" and either put the casinos out of business or force them to change the rules of the game (or ban craps)?

Casino's have bad days, sometimes they have very bad days. Sometimes, a whale comes in and happens to win big, taking a given "house" for a ride, and they end up posting a loss in their accounting books. When that occurs, that is just a case of variance swinging very wildly in the player's favor for a period of time. The mathematics of these casino games, where the payoffs are typically not true odds, are such that over time, the Casinos stands to make money on every game and every individual wager they offer. As I said at during the original post for this thread, the best-case (rare) scenario is that a Casino offers a payoff for a wager at true odds (example: No Vig buy bets on 4 or 10, field paying triple on 3 or 12) In those rare cases, the casino is still not worried because they don't stand to loose money...rather the math of such bets is such that statistically, they will break even for offering those rare zero EV bets.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by DanF » Mon May 21, 2018 2:06 pm

It’s no fool proof like any. But you get to hit your win goal fast on good days, loss limit even faster on bad ones.

You don’t have to try it. But It suits my fun needs.

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by mainframe » Mon May 21, 2018 4:38 pm

DanF: I was only commenting on a game of craps with unbiased, truly random dice without controlled shooters/dice influeners.
In a truly random game of craps, such as an electronic version with a truly unbiased random number generator, no betting system will net a positive result in the long run, over a large number of trials (rolls). If you only make a single line bet with no odds, the EV=-1.41%. That means (in a fully, true random game, you can expect to loose $1.41 for every $100 wagered. For any given bet, the long-term results will approach the EV for that bet.
Now with Dice Influence in play, you may be able to wager in such a way that plays to the strengths in your dice influencing ability. For example, if you have practiced a lot and have a knack for rolling sevens, you can play DP/DC and hope for better outcomes than the mathematical house edge.
If your system seems to work well with your controlled shooting, that's great.
Irish: As far as your statement we've debunked "Losing less = winning more.", could you point me to thread regarding regression betting results combined with Dice Influence? I would think it is question of semantics? If you define a winning session as "any session that ends where your bankroll has increased, even in the slightest", then maybe a regression-based strategy leads to more winning sessions, if not "winning more" (meaning, a higher net gain in session bankroll over a regression-based strategy).
If I may hazard a non-math backed guess:
Less money wagered over less trials = less starting bankroll exposed less to the law of large numbers = higher variance in outcomes
(with the distinct possibility that variance works in player's favor)
With regression betting, the same principle applies. You expose a larger stake (wager) for a smaller number of trials, followed by a smaller stake (wager) for some additional trials (events). All you are doing is exposing less money over time than a fixed larger wager that is not regressed after a certain number of hits.

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Big O
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Re: Law of Large Numbers, Variance, bet size/frequency

Post by Big O » Mon May 21, 2018 8:02 pm

"There's no crystal ball, or system for predicting variance so that you can apply a strategy ahead of time."
This statement addresses something i have been struggling with for some time. There are numerous threads and post about planning your strategy before you get to the table and and sticking to it until you hit your win goal or stop loss. My problem is i dont feel like i have developed any plan of attack that i trust enough to always play the same way regardless of what happens at the table. Especially before i watch the other shooters toss or at least toss the dice myself to see how everything feels.

My first year playing craps i played/bet very conservatively. Partly from not wanting to lose, but more so from just not knowing how to bet. Fortunately this approach was successful and allowed me to learn and win at the same time. As i learned more about the game i decided if i could build my bank roll to a certain point i would go to the tables with a much more aggressive style. I may have jumped the gun a little before i reached my bank roll goal but i was very close so i made the jump.

So far results have not been good. Even though i feel my game has improved in every facet the wins have been hard to come by. I certainly believe there is no crystal ball and there is not a system that can beat the game with enough regularity to depend on it. I do know that if you expose too much money for too long you will lose.
"if it was easy anyone could do it"

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Re: Law of Large Numbers, Variance, bet size/frequency

Post by skasower » Tue May 22, 2018 5:00 pm

Very cogent responses Mr. Irish. Clearly we practice DI in hopes of not being another Randy. I am still hoping that I can figure out early on that I am watching a stranger toss who herself is a DI aficionado. That way, I am in the game and not charging my bankroll to "entertainment" alone, while waiting to get the dice and to toss myself.

One quick disclaimer: I am yet not sure that I am a dependable DI. My practice is daily since January and I have moments where it really "clicks" and wonderful tosses follow wonderful tosses. Then there are times when I even embarrass myself (all practicing at home, not out in the wild).

The Law of Age Numbers reminds me of the John Milton Keynes quote about economists who look at the long term. Keynes said, in the long term we are all dead. And so would go your bankroll betting on Randys.

skasower...aka...
Profe$$or Ka$hFi$h

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